Bastiaan S. Veeling

Phillip Lippe, Bastiaan S. Veeling, Paris Perdikaris et al.

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained increased interest. The practical utility of such neural PDE solvers relies on their ability to provide accurate, stable predictions over long time horizons, which is a notoriously hard problem. In this work, we present a large-scale analysis of common temporal rollout strategies, identifying the neglect of non-dominant spatial frequency information, often associated with high frequencies in PDE solutions, as the primary pitfall limiting stable, accurate rollout performance. Based on these insights, we draw inspiration from recent advances in diffusion models to introduce PDE-Refiner; a novel model class that enables more accurate modeling of all frequency components via a multistep refinement process. We validate PDE-Refiner on challenging benchmarks of complex fluid dynamics, demonstrating stable and accurate rollouts that consistently outperform state-of-the-art models, including neural, numerical, and hybrid neural-numerical architectures. We further demonstrate that PDE-Refiner greatly enhances data efficiency, since the denoising objective implicitly induces a novel form of spectral data augmentation. Finally, PDE-Refiner's connection to diffusion models enables an accurate and efficient assessment of the model's predictive uncertainty, allowing us to estimate when the surrogate becomes inaccurate.

Marco Federici, Patrick Forré, Ryota Tomioka et al.

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.

Jason Yim, Andrew Campbell, Emile Mathieu et al.

Protein design often begins with the knowledge of a desired function from a motif which motif-scaffolding aims to construct a functional protein around. Recently, generative models have achieved breakthrough success in designing scaffolds for a range of motifs. However, generated scaffolds tend to lack structural diversity, which can hinder success in wet-lab validation. In this work, we extend FrameFlow, an SE(3) flow matching model for protein backbone generation, to perform motif-scaffolding with two complementary approaches. The first is motif amortization, in which FrameFlow is trained with the motif as input using a data augmentation strategy. The second is motif guidance, which performs scaffolding using an estimate of the conditional score from FrameFlow without additional training. On a benchmark of 24 biologically meaningful motifs, we show our method achieves 2.5 times more designable and unique motif-scaffolds compared to state-of-the-art. Code: https://github.com/microsoft/protein-frame-flow

Lizeth Gonzalez-Carabarin, Iris A. M. Huijben, Bastiaan S. Veeling et al.

Unstructured neural network pruning algorithms have achieved impressive compression rates. However, the resulting - typically irregular - sparse matrices hamper efficient hardware implementations, leading to additional memory usage and complex control logic that diminishes the benefits of unstructured pruning. This has spurred structured coarse-grained pruning solutions that prune entire filters or even layers, enabling efficient implementation at the expense of reduced flexibility. Here we propose a flexible new pruning mechanism that facilitates pruning at different granularities (weights, kernels, filters/feature maps), while retaining efficient memory organization (e.g. pruning exactly k-out-of-n weights for every output neuron, or pruning exactly k-out-of-n kernels for every feature map). We refer to this algorithm as Dynamic Probabilistic Pruning (DPP). DPP leverages the Gumbel-softmax relaxation for differentiable k-out-of-n sampling, facilitating end-to-end optimization. We show that DPP achieves competitive compression rates and classification accuracy when pruning common deep learning models trained on different benchmark datasets for image classification. Relevantly, the non-magnitude-based nature of DPP allows for joint optimization of pruning and weight quantization in order to even further compress the network, which we show as well. Finally, we propose novel information theoretic metrics that show the confidence and pruning diversity of pruning masks within a layer.

Iris A. M. Huijben, Bastiaan S. Veeling, Ruud J. G. van Sloun

Compressed sensing (CS) MRI relies on adequate undersampling of the k-space to accelerate the acquisition without compromising image quality. Consequently, the design of optimal sampling patterns for these k-space coefficients has received significant attention, with many CS MRI methods exploiting variable-density probability distributions. Realizing that an optimal sampling pattern may depend on the downstream task (e.g. image reconstruction, segmentation, or classification), we here propose joint learning of both task-adaptive k-space sampling and a subsequent model-based proximal-gradient recovery network. The former is enabled through a probabilistic generative model that leverages the Gumbel-softmax relaxation to sample across trainable beliefs while maintaining differentiability. The proposed combination of a highly flexible sampling model and a model-based (sampling-adaptive) image reconstruction network facilitates exploration and efficient training, yielding improved MR image quality compared to other sampling baselines.

Jakub Swiatkowski, Kevin Roth, Bastiaan S. Veeling et al.

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the approximate posterior in the hope of improving performance. In contrast, here we share a curious experimental finding that suggests instead restricting the variational distribution to a more compact parameterization. For a variety of deep Bayesian neural networks trained using Gaussian mean-field variational inference, we find that the posterior standard deviations consistently exhibit strong low-rank structure after convergence. This means that by decomposing these variational parameters into a low-rank factorization, we can make our variational approximation more compact without decreasing the models' performance. Furthermore, we find that such factorized parameterizations improve the signal-to-noise ratio of stochastic gradient estimates of the variational lower bound, resulting in faster convergence.

Florian Wenzel, Kevin Roth, Bastiaan S. Veeling et al.

During the past five years the Bayesian deep learning community has developed increasingly accurate and efficient approximate inference procedures that allow for Bayesian inference in deep neural networks. However, despite this algorithmic progress and the promise of improved uncertainty quantification and sample efficiency there are---as of early 2020---no publicized deployments of Bayesian neural networks in industrial practice. In this work we cast doubt on the current understanding of Bayes posteriors in popular deep neural networks: we demonstrate through careful MCMC sampling that the posterior predictive induced by the Bayes posterior yields systematically worse predictions compared to simpler methods including point estimates obtained from SGD. Furthermore, we demonstrate that predictive performance is improved significantly through the use of a "cold posterior" that overcounts evidence. Such cold posteriors sharply deviate from the Bayesian paradigm but are commonly used as heuristic in Bayesian deep learning papers. We put forward several hypotheses that could explain cold posteriors and evaluate the hypotheses through experiments. Our work questions the goal of accurate posterior approximations in Bayesian deep learning: If the true Bayes posterior is poor, what is the use of more accurate approximations? Instead, we argue that it is timely to focus on understanding the origin of the improved performance of cold posteriors.

Linh Tran, Bastiaan S. Veeling, Kevin Roth et al.

Ensembles of models have been empirically shown to improve predictive performance and to yield robust measures of uncertainty. However, they are expensive in computation and memory. Therefore, recent research has focused on distilling ensembles into a single compact model, reducing the computational and memory burden of the ensemble while trying to preserve its predictive behavior. Most existing distillation formulations summarize the ensemble by capturing its average predictions. As a result, the diversity of the ensemble predictions, stemming from each member, is lost. Thus, the distilled model cannot provide a measure of uncertainty comparable to that of the original ensemble. To retain more faithfully the diversity of the ensemble, we propose a distillation method based on a single multi-headed neural network, which we refer to as Hydra. The shared body network learns a joint feature representation that enables each head to capture the predictive behavior of each ensemble member. We demonstrate that with a slight increase in parameter count, Hydra improves distillation performance on classification and regression settings while capturing the uncertainty behavior of the original ensemble over both in-domain and out-of-distribution tasks.

Iris A. M. Huijben, Bastiaan S. Veeling, Kees Janse et al.

Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted considerable attention in recent years. Compressed sensing emerged as a popular framework for sparse signal reconstruction from a small set of compressed measurements. However, typical compressed sensing designs measure a (non)linearly weighted combination of all input signal elements, which poses practical challenges. These designs are also not necessarily task-optimal. In addition, real-time recovery is hampered by the iterative and time-consuming nature of sparse recovery algorithms. Recently, deep learning methods have shown promise for fast recovery from compressed measurements, but the design of adequate and practical sensing strategies remains a challenge. Here, we propose a deep learning solution termed Deep Probabilistic Sub-sampling (DPS), that learns a task-driven sub-sampling pattern, while jointly training a subsequent task model. Once learned, the task-based sub-sampling patterns are fixed and straightforwardly implementable, e.g. by non-uniform analog-to-digital conversion, sparse array design, or slow-time ultrasound pulsing schemes. The effectiveness of our framework is demonstrated in-silico for sparse signal recovery from partial Fourier measurements, and in-vivo for both anatomical image and tissue-motion (Doppler) reconstruction from sub-sampled medical ultrasound imaging data.

Sindy Löwe, Peter O'Connor, Bastiaan S. Veeling

We propose a novel deep learning method for local self-supervised representation learning that does not require labels nor end-to-end backpropagation but exploits the natural order in data instead. Inspired by the observation that biological neural networks appear to learn without backpropagating a global error signal, we split a deep neural network into a stack of gradient-isolated modules. Each module is trained to maximally preserve the information of its inputs using the InfoNCE bound from Oord et al. [2018]. Despite this greedy training, we demonstrate that each module improves upon the output of its predecessor, and that the representations created by the top module yield highly competitive results on downstream classification tasks in the audio and visual domain. The proposal enables optimizing modules asynchronously, allowing large-scale distributed training of very deep neural networks on unlabelled datasets.

Bastiaan S. Veeling, Rianne van den Berg, Max Welling

High-risk domains require reliable confidence estimates from predictive models. Deep latent variable models provide these, but suffer from the rigid variational distributions used for tractable inference, which err on the side of overconfidence. We propose Stochastic Quantized Activation Distributions (SQUAD), which imposes a flexible yet tractable distribution over discretized latent variables. The proposed method is scalable, self-normalizing and sample efficient. We demonstrate that the model fully utilizes the flexible distribution, learns interesting non-linearities, and provides predictive uncertainty of competitive quality.

Jasper Linmans, Jim Winkens, Bastiaan S. Veeling et al.

We propose a semantic segmentation model that exploits rotation and reflection symmetries. We demonstrate significant gains in sample efficiency due to increased weight sharing, as well as improvements in robustness to symmetry transformations. The group equivariant CNN framework is extended for segmentation by introducing a new equivariant (G->Z2)-convolution that transforms feature maps on a group to planar feature maps. Also, equivariant transposed convolution is formulated for up-sampling in an encoder-decoder network. To demonstrate improvements in sample efficiency we evaluate on multiple data regimes of a rotation-equivariant segmentation task: cancer metastases detection in histopathology images. We further show the effectiveness of exploiting more symmetries by varying the size of the group.

Bastiaan S. Veeling, Jasper Linmans, Jim Winkens et al.

We propose a new model for digital pathology segmentation, based on the observation that histopathology images are inherently symmetric under rotation and reflection. Utilizing recent findings on rotation equivariant CNNs, the proposed model leverages these symmetries in a principled manner. We present a visual analysis showing improved stability on predictions, and demonstrate that exploiting rotation equivariance significantly improves tumor detection performance on a challenging lymph node metastases dataset. We further present a novel derived dataset to enable principled comparison of machine learning models, in combination with an initial benchmark. Through this dataset, the task of histopathology diagnosis becomes accessible as a challenging benchmark for fundamental machine learning research.

Stojan Trajanovski, Dimitrios Mavroeidis, Christine Leon Swisher et al.

Importance: Lung cancer is the leading cause of cancer mortality in the US, responsible for more deaths than breast, prostate, colon and pancreas cancer combined and it has been recently demonstrated that low-dose computed tomography (CT) screening of the chest can significantly reduce this death rate. Objective: To compare the performance of a deep learning model to state-of-the-art automated algorithms and radiologists as well as assessing the robustness of the algorithm in heterogeneous datasets. Design, Setting, and Participants: Three low-dose CT lung cancer screening datasets from heterogeneous sources were used, including National Lung Screening Trial (NLST, n=3410), Lahey Hospital and Medical Center (LHMC, n=3174) data, Kaggle competition data (from both stages, n=1595+505) and the University of Chicago data (UCM, a subset of NLST, annotated by radiologists, n=197). Relevant works on automated methods for Lung Cancer malignancy estimation have used significantly less data in size and diversity. At the first stage, our framework employs a nodule detector; while in the second stage, we use both the image area around the nodules and nodule features as inputs to a neural network that estimates the malignancy risk for the entire CT scan. We trained our two-stage algorithm on a part of the NLST dataset, and validated it on the other datasets. Results, Conclusions, and Relevance: The proposed deep learning model: (a) generalizes well across all three data sets, achieving AUC between 86% to 94%; (b) has better performance than the widely accepted PanCan Risk Model, achieving 11% better AUC score; (c) has improved performance compared to the state-of-the-art represented by the winners of the Kaggle Data Science Bowl 2017 competition on lung cancer screening; (d) has comparable performance to radiologists in estimating cancer risk at a patient level.